Just finished the 1861 Campaign as CSA:
Or, perhaps a better turn of phrase would be, it finished itself.
Made it to Jan 1864, and it ended in a stalemate. CSA morale was 148 (max. 175), and USA was 55 (min. 60). (I blame it on McClellan winning the 1864 election).
This was with Detection Bonus Low / AI with extra time / Normal Agression / Use all behaviors.
My strategy as the South was to basically adopt a defensive stance in the East, take Kentucky and Missouri in the West, and let the Union come to me. Fortunately (or not), the Union AI doesn't seem up to the task, and other than a few faints toward Harper's Ferry, or at Alexandria, the only major invasions I've had to deal with were at Norfolk, while the Union Navy ineffectually bombards my coastal forts. The AI seems adept enough at creating large formations, it just doesn't want to use them --- or sends them off piecemeal.
As the CSA player, my biggest problem was in the money / conscripts area. But once I started launching 25 - 30 blockade runners, and alternating between the three financial options, money became manageable. And since combat was minimal, the replacement problem was too. I started the game with two armies, and only got around to creating a third in 1863. Most of my offensive effort went into long-range cavalry raids into Union territory, tearing up rail lines --- which the AI has yet to repair.
I'd say that most of my effort has gone into raising the Industrialization Level, Rail Capacity, River Transport Capacity, while building up my (defensive) military formations.
I'm waiting for the next big update before starting a game as the USA --- perhaps the AI can handle defense better than offense.